GG -- the Grassmannian of k-dimensional linear subspaces of an n-dimensional projective space

• Usage:

  GG(k,PP_K^n)

  GG_K(k,n)

  GG Grass(k,n,K,Variable=>"x")

• Inputs:
  • k, an integer
  • P, an embedded projective variety, a projective space of dimension $n$
• Outputs:
  • a Grassmannian variety, which parametrizes the $k$-dimensional subspaces of $\mathbb{P}^n$

i1 : GG(2,PP_QQ^5)

o1 = GG(2,5) ⊂ PP^19

o1 : ProjectiveVariety, GG(2,5)

i2 : describe oo

o2 = ambient:.............. PP^19
     dim:.................. 9
     codim:................ 10
     degree:............... 42
     generators:........... 2^35 
     purity:............... true
     dim sing. l.:......... -1